The impact of price elasticity in the sales and operations planning

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Bachelor Thesis

The impact of price elasticity

in the sales and operations planning

.

Robert van Steenbergen Enschede

Industrial Engineering & Management July, 2017

PUBLIC VERSION

In this public version, the names of the company

and products are replaced by fictive names. Some

sections and figures are adjusted or completely

removed. Due to the anonymisation, there may be

inconsistencies in the data and calculations.

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Company X

Document title

Status Date Author

The impact of price elasticity in the sales and operations planning Bachelor thesis for the bachelor program Industrial Engineering and Management at the University of Twente

Public report 20-07-2017

R.M. van Steenbergen rmvsteen@gmail.com

Graduation committee University of Twente

Company X

Dr. M.C. van der Heijden

Faculty of Behavioural Management and Social Sciences

Department Industrial Engineering and Business Information Systems

Dr. ir. L.L.M. van der Wegen

Faculty of Behavioural Management and Social Sciences

Department Industrial Engineering and Business Information Systems

Sales and Operations planner Department X

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Management summary

The monthly allocation of the raw material at Company X (further referred to as CX) is planned with a sales and operations planning (S&OP) model. The S&OP model allocates the raw material to aggregated product categories, so-called plan products. Around 20% of the total raw material supply is processed into the plan product ‘product 1’.

CX has a market share of more than 50% in product 1 and their production quantities influence the market price. The effect between quantity and price is usually expressed in the term price elasticity.

Currently, CX does not consider the effect of price elasticity in their S&OP model. Previous research expresses the relation between quantity and price mathematically and shows positive results in a fictional case study with piecewise linear approximations. Piecewise linear approximations are necessary to implement price elasticity in the S&OP model of CX. This research investigates the impact of implementing price elasticity in the actual S&OP model with real data of CX. Therefore, the main research question of this thesis is:

What is the impact of the implementation of price elasticity in the sales and operations model of Company X?

At first, we investigate the current situation. Processing raw material into product 1 results in the by- production of product 3 and product 4. The same applies for the processes other products, like product 2, which results in the by-production of product 4. To measure the valorisation, or added value, for processing raw material into a certain products and corresponding by-products, CX categorised its products and by-products in certain ‘baskets’. We will analyse the financial effects of the products with the change of the valorisation of these baskets due to price elasticity.

The analysis of the current situation is followed by a literature review about price elasticity in sales and operations planning. The literature shows positive results. However, it does not provide a direct answer to our main research question. In additional to the literature review, we find a general approach for piecewise linear approximations. We adopt the general approach from the literature to construct piecewise linear approximations of the revenue curve of product 1.

Then, we specify the details of the piecewise linear approximation of product 1 and adjust the S&OP model to implement the new prices and quantities. The main assumption and therefore the main limitation of this research is that we only consider the effect price elasticity at product 1 and assume that all other factors remain constant. We assume that competitors do not respond to the decisions of CX and that the demand and prices of other products do not change. We assume that prices of product 1 only respond to the quantity of the same month.

After we made the assumptions and implemented price elasticity, we investigate the impact of price elasticity in the S&OP model. By means of experiments, we find that a model with 10 segments provides adequate accuracy for the implementation of price elasticity. The model with price elasticity suggests to reduce the annual product 1 quantity with 4.1% and to increase the product 2 quantity with 11.8% compared to the current model. This change results in an annual improvement of the valorisation of 68 thousand euros, which is 0.52% of the revenue of product 1, product 2 and corresponding by-products.

The impact of price elasticity is significantly higher in months in which the valorisation of product 1 is low relative to the valorisation of product 2. Therefore, the impact of price elasticity can significantly improve when the valorisation of product 1 and product 2 become closer to each other than in the current market situation.

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The sensitivity analysis shows that the financial improvement is nullified when the forecasted prices of product 1 and product 2 deviate with 6 to 10% over the whole year. Because these situations are highly unlikely, the improvements in valorisation have a low risk regarding the input data. However, we discover larger risks from the worst-case scenario. Then, a loss of 220 thousand euros can be made due to change in quantity of product 1 to product 2. The worst-case scenario shows a lower risk in months in which the valorisation of product 1 is low relative to the valorisation of product 2 and confirms the increased potential of these months.

Although the annual financial improvement of price elasticity is 68 thousand in our research, we do not recommend starting to use price elasticity as it is used in this research. We do not recommend this, because we assume in this study that competitors do not response and that the prices only react on the quantity of the same month. However, these assumptions are not consistent with reality and thus limit the practical feasibility of this research. In the worst-case scenario, CX makes an expected loss of 220 thousand euros. Nevertheless, the results of price elasticity are more promising when the valorisation of product 1 becomes low relative to the product 2 valorisation. Therefore, we recommend combining the concepts of this study with more knowledge about the product 1 market to benefit from the effects of price elasticity when the valorisation of product 1 becomes close to the product 2 valorisation.

As future research, we suggest to extend the S&OP model with more intelligent market behaviour.

We recommend investigating how to implement the response of competitors, enhanced price behaviour and price elasticity of other products into the S&OP model, while keeping the human effort for the S&OP within bounds.

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Preface

To complete the bachelor Industrial Engineering & Management at the University of Twente, I performed at in-depth research assignment at Company X about the impact of price elasticity on their sales and operations planning. The findings of this study are reported in this bachelor thesis.

For the past three month I worked at Company X at Department X. This gave me the opportunity to experience the complexity and possibilities of the supply chain and planning of Company X. I gained a lot of knowledge about these processes during my time at Department X. I would like to thank my colleagues for the interesting conversations and their help during my research.

This report would not be here without the support of my supervisors. At first, I would like to thank my supervisor at Company X. He guided me through the research and we had valuable discussions about the ideas and insights of this study. I would also like to thank Matthieu van der Heijden, my supervisor from the University of Twente, for his valuable feedback and scientific insights.

Finally, I would like to thank my friends and family for their support during this research.

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List of figures and tables

Figure 1.1 - The S&OP process divides the raw material over the S&OP hubs ... 1

Figure 2.1 - Revenue curves for one month of methods without and with price elasticity ... 6

Figure 2.2 - The demand system with three segments ... 7

Figure 2.3 - Structure of the modelled supply chain of product 1 ... 8

Figure 2.4 - Basic calculation for the valorisation ... 8

Figure 2.5 - Example of an equivalence table ... 9

Figure 3.1 - Overlap between the topics ... 10

Figure 3.2 - Example of a piecewise linear approximation ... 13

Figure 4.1 - Influence on revenue of product 1 ... 15

Figure 4.2 - The underestimation equal to the overestimation (a) and the maximum deviation in the middle of a segment (b) ... 17

Figure 4.3 - Approximations in the relevant area ... 18

Figure 4.4 - The current model (a) and the model extended with price elasticity (b) ... 20

Figure 4.5 - Black-box validation (Robinson, 2004) ... 21

Figure 4.6 - Comparison between the models ... 22

Figure 4.7 - Hierarchy of the product 1 basket ... 23

Figure 4.8 - Quantity and price effect ... 24

Figure 5.1 - Accuracy of the approximations... 28

Figure 5.2 - Accuracy of the number of segments ... 29

Figure 5.3 - Expected improvement of the valorisation per month ... 31

Figure 5.4 - Effects in July 2017 (a) and December 2018 (b) ... 31

Figure 5.5 - Equivalence table of product 2 and additional product 1 ... 32

Figure 5.6 - Sensitivity analysis ... 33

Figure 5.7 - Potential improvement and worst-case loss ... 34

Figure 5.8 - Equivalence table with product 2, product 1 and raw material sales ... 36

Table 3.1 - Classification of the effects of price elasticity ... 11

Table 4.1 - Characteristics of the piecewise linear approximation ... 27

Table 5.1 - Annual changes in the S&OP due to price elasiticty... 30

Table 5.2 - Annual effects of the valorisation ... 30

Table 5.3 – Worst-case annual financial effects ... 34

Table 5.4 – Annual changes in the S&OP due to a varying capacity ... 36

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Glossary

Basket A group of products consisting of a main product and corresponding by-products to which raw material can be allocated and completely processed.

Disturbance capacity Spare capacity planned to anticipate on disturbances

ET Equivalence table

CX Company X

Hub S&OP division of Company X

Raw material flow The amount of raw material allocated to a certain basket P-effect The financial effect in revenue caused by a change in price

Plan product Aggregated product category consisting of products with comparable production processes and market behaviour

Price elasticity Change in price caused by the change in quantity

Q-effect The financial effect in revenue casued by a change in quantity Raw material-product 1 ratio The ratio of additional raw material sales which ends up in product 1

S&OP Sales and Operations Planning

Valorisation The process of creating value or adding value to a product

VBA Visual Basic for Applications, the programming language within Microsoft® Excel

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1. Introduction

In this chapter, we introduce the research conducted at Department X of Company X. The research investigates the effects of implementing price elasticity in the Sales and operations Planning model.

At first, we give a brief description of Company X, Department X and the Sales and operations Planning process. We describe previous research at Company X about price elasticity. Afterwards we describe the aim of this research with the problem statement, relevance, scope and research questions.

1.1. Company X

CONFIDENTIAL Department X CONFIDENTIAL

Sales & Operations Planning

With the monthly Sales & Operations Planning (S&OP) process, CX determines for the coming 18 months how to allocate the raw material supply in a product mix that adds the most value, given the capacity, the raw material supply and the market. CX has to process all raw material supplied.

Therefore, the S&OP is an important process to balance supply and demand. To make optimal decisions, the S&OP planners use an S&OP tool in which the supply chain of CX is modelled on an aggregated level. The S&OP tool financially optimizes the planning.

The process is a close collaboration between Department X and 10 S&OP divisions of CX, called

‘hubs’. Those hubs have their own product category (e.g. product 1 or product 2). Hubs are not location specific and multiple hubs can serve one factory. For example, a factory can make product 1, product 2 and product 3, all planned by another hub.

The S&OP process brings the information of those hubs together to distribute the raw material in the most valorising way and therefore prevents the negative effects of local optimization of the hubs.

The hubs provide Department X with their aggregated demand volumes, available production hours and sales prices for the coming 18 months. Besides the information of the hubs, the forecast of the raw material supply and the external raw material sales are used. The output of the S&OP process is a plan which allocates the raw material to the hubs and their aggregated product categories, called plan products.

CONFIDENTIAL

Figure 1.1 - The S&OP process divides the raw material over the S&OP hubs

Previous research

Previously, Company X worked together with Wageningen University to test and implement a new S&OP tool and investigate the practical and financial feasibility of including price elasticity.

The research of Van Haperen (2016) concluded that all necessary functionalities are present in the new tool to implement price elasticity. A fictional case study was performed and shows a significant financial improvement. Van Haperen (2016) concluded that further research is needed with actual data of Company X. He also stated that piecewise linear approximations are necessary to implement price elasticity in the S&OP model. Van Haperen (2016) expressed the relationship between the change in price and the change in quantity as follows.

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For every decrease in quantity , the sales price increases with a constant value :

∆ = −∆ ∗ (1)

In which:

∆ = Change in price

∆ = Change in quantity ( − ) = Price elasticity constant

With this value for the extent to which the price changes caused by changes in quantity, Van Haperen (2016) expressed the relationship between the produced quantity and the sales price mathematically.

= − ∗ + ∗ + ∗ (2)

In which:

= Revenue

= Price elasticity constant = Quantity

= Initial quantity = Initial sales price

With (2) Van Haperen (2016) included the effect of price elasticity in the revenue function. Appendix A clarifies the complete derivation of this expression. This equation is very useful, because the initial quantity and the initial sales price for every month are reported by CX.

1.2. Problem statement

The Market Intelligence department of CX investigates the markets in which CX operates. They observe that the sales volumes of CX of product 1, product 7 and product 11 have influence on their price in the markets, especially within the product 1 market. When additional volumes are pushed on the market, a downwards price effect is observed over the whole volume. The relation between quantity and price is usually expressed in term price elasticity. Price elasticity is defined as the ratio of the percentage change in quantity to the percentage change in price (Case, Fair, & Oster, 2011).

Throughout this report, the term ‘price elasticity’ is used to refer to the change in price caused by the change in quantity. This effect is not yet considered in the S&OP process, while the research of Van Haperen (2016) shows a significant financial improvement in a fictional case study. Besides the potential, required data and technical possibilities are available.

Currently, the hubs provide an average sales price and sales prices when the quantity changes with -10% and +10%. According to the business controller of Department X who responsible for gathering the sales prices for the S&OP, the average sales prices are accurate, but the ±10% prices are based on intuition rather than facts or calculations. To improve the price and revenue in the S&OP process, Department X wants to investigate a new approach which considers the price elasticity of a product.

Currently, the hubs provide an average sales price and sales prices when the quantity changes with -5% and +5%. According to the controlling analyst of the MVA who responsible for gathering the sales prices for the E S&OP, the average sales prices are accurate, but the ±5% prices are based on intuition rather than facts or calculations. To improve the price and revenue estimations in the E S&OP process, the MVA wants to investigate a new approach which considers the price elasticity of a product.

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The main problem is that CX has no insight in the impact of the implementation of price elasticity within the actual S&OP model. They believe that the more accurate approach of price elasticity will result in a better valorisation, which means that CX can add more value to the supplied raw material.

Therefore, the price elasticity approach should be implemented and the effects of the implementation should be investigated to solve the problem.

1.3. Relevance

The S&OP model plans every month how nearly 1 million kilos raw material will be processed and sold. From this amount, around 20% will be processed into product 1. Therefore, it is expected that a small improvement in the S&OP model changes the allocation of thousands of kilos raw material.

Because improving the model can have a large impact, it is important to investigate the effects with this study.

With the current model, prices regarding the additional volumes in the product 1 market are inaccurate. Especially too high price estimations by the model can result in selling product 1 for lower prices than expected. This situation is undesirable for CX, because they lose money due to the lower prices. They may even sell their product 1 below the cost price. The raw material used for the production of product 1 could have been used for better purposes with a higher valorisation. The implementation of price elasticity can prevent such situations.

1.4. Scope

The S&OP model considers a lot of plan products. It is impossible for this project to implement the price elasticity for all products for which price elasticity is observed. Therefore, the scope of the study is the price elasticity of product 1. The Market Intelligence department knows the value of price elasticity in the product 1 market and product 1 covers a large share of the production volume of CX. We exclude price elasticity of other products in this research.

The focus of the project is to implement price elasticity into the S&OP model for the product 1 market and analyse the effects of this implementation. It is important to investigate the potential financial improvements and to find out how decision-making changes within the S&OP model. All required data, such as the value for price elasticity, demand data and sales prices, is available and we take these data as given. Therefore, market research on the price elasticity is outside the scope of this research. Organizational implications due to the implementation of price elasticity, such as changing information flows, are out of scope.

1.5. Research questions

The main problem of Department X is that they do not know which impact the implementation of price elasticity will have on the sales and operations planning and financial results. The objective of this research project is to implement the effect price elasticity at product 1 in the S&OP model and to investigate the effects of the planning and valorisation. The described objective leads to the following main research question:

What is the impact of the implementation of price elasticity in the sales and operations model of Company X?

To provide insight into the impact of the implementation of price elasticity, we answer four sub questions.

1. How does Company X currently manage demand in the S&OP process?

Chapter 2 describes the current situation. To adjust and improve the S&OP model with price elasticity, we first provide insight into the current situation. We investigate the relevant markets and the current revenue curve. We also elaborate about the way of managing demand and the current

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model of CX. Furthermore, we elaborate about the methods CX uses to analyse the valorisation of their products.

2. What literature is available related to the use and implementation of price elasticity in sales and operations planning of Company X?

We answer this question in Chapter 3. We investigate the concepts of sales and operations planning, oligopoly and price elasticity. We use a systematic literature review protocol to answer the research question and provide insight into the impact of price elasticity according to literature. We also study literature about piecewise linear approximations to support the implementation of price elasticity in the S&OP model.

3. How should we adjust the S&OP model to implement the price elasticity of product 1?

In Chapter 5 we elaborate about the adjustments of the model necessary for this research. At first, we investigate the influences in the market to implement price elasticity correctly. We determine the characteristics of the piecewise linear approximation of product 1. We will also list our simplifications and assumptions and validate the model. We also describe the actual adjustments and implementation of the model and explain our key performance indicators.

4. What is the impact of price elasticity on decision-making and the valorisation of the S&OP model?

In Chapter 6 we describe the numerical results of the impact of the implementation of price elasticity. Due to price elasticity, both decisions and the valorisation change. To gain broad understanding of the model and the effects of price elasticity, we perform experiments with a different number of segments, perform a sensitivity analysis and a worst-case scenario. We also investigate several scenarios.

After we answered all research questions, we draw conclusions, mention the limitations of this research and provide recommendations and future research. At the end of the report are appendices which provide additional information about this research.

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2. Current situation

In this chapter, we describe which aspects are involved in managing the demand in the S&OP process. We answer the first research question:

How does Company X currently manage demand in the S&OP process?

In this section, we investigate the relevant markets, the current revenue curve and describe the demand and supply chain modelling of the S&OP model. We also discuss the concept of equivalence tables, which is used to evaluate the valorisation of different products.

2.1. Relevant products and markets

We focus for this research on two main products, product 1 and product 2. Product 2 is a common alternative of product 1 regarding the processing of raw material. Both products are important to balance the supply and demand of CX. They are produced in high volumes with low margins and making a loss on these products is not uncommon. Therefore, small improvements have a significant impact on the profit. Although product 1 and product 2 are used for the same purpose, the market characteristics of the two products are totally different.

The product 1 market is a small market in which CX competes with mainly smaller national companies. Company X has a market share of over 50%. Due to the large market share, CX can significantly influence the market price with its own volumes. Decreasing the product 1 production leads to a shortage in the market and increases prices. Because relatively few companies produce product 1, which are large enough to influence the market price, we characterise the product 1 market as an oligopolistic market.

On the other hand, the product 2 market is a large global market in which CX competes with a lot of companies around the world. Although CX is large company in the Netherlands, in the world they only have a market share of 6%. The quantities of CX do not significantly influence the market price.

We can characterise the product 2 market a market with almost perfect competition, because it is a market with a lot of suppliers which cannot individually influence the market price.

2.2. Current revenue curve

As described in Section 1.2, the hubs currently provide an average sales price of the current quantity and sales prices when the quantity changes with -10% or +10%. When we analyse the planned sales prices of product 1, we see that the average price, the -10% and +10% prices are equal in each month. Therefore, the downwards price effect is not considered at this moment by the product 1 hub. When we consider the more accurate method with price elasticity, the revenue has a downward slope. Figure 2.1 shows the revenue curve for one month of the current method and the revenue curve when price elasticity is included. The revenues are quite close to each other near the current production quantity of ±2,000 tons. However, at a quantity of 2,500 tons is the deviation between the two methods already 10 thousand euros. This deviation leads to sub optimal decisions in the S&OP plan.

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Figure 2.1 - Revenue curves for one month of methods without and with price elasticity

We do not plot historic data in Figure 2.1 to analyse the accuracy of the revenue curve with price elasticity. The price and revenue are dependent on a lot of more factors than the production quantity of CX. Due to constantly changing market conditions (e.g. governmental regulations and the world raw material supply), the historic data cannot provide an unbiased result. On top of that, market analysis is out of the scope of this research. We take the price elasticity as given and reliable, provided by the Market Intelligence department of CX. Their insight into the markets and price elasticity is far beyond the reach of this research project. Nevertheless, in this project we manage the potential inaccuracy with the sensitivity analysis in Chapter 5.

2.3. S&OP tool

CX is currently developing and implementing a new S&OP tool to support the S&OP process. The S&OP tool is a deterministic tool which consists of multiple coherent tables to model a supply chain.

Currently, there are tables present for all main characteristics of the supply chain, among others the raw material supply, factories, products, machines and customers. At the background of the tool runs a linear programming solver to find the financially optimal solution. Not all supply chains and products are modelled at the moment of this research.

Because of a linear solver and tables in which we need to fill prices and quantities, we cannot implement mathematical functions like the revenue curve. Therefore, Van Haperen (2016) stated that CX has to apply piecewise linear approximations to implement the revenue curve in the S&OP tool. Instead of one price for a product, we can divide the demand in several segments. By using multiple tables, we can provide different prices at certain volumes and approximate the revenue curve.

2.4. Demand modelling in the S&OP tool

At this moment is the demand of the products in the S&OP tool is divided into three segments, with corresponding quantities and sales prices. The segments are called the fixed, the reducible and the additional segment. The S&OP process cannot adjust the quantity of the fixed segment, but it can change the quantities of the reducible and additional demand.

The S&OP model is obliged to fulfil the fixed demand, due to a high valorisation of the products or contractual agreements with customers. The reducible demand and the additional demand give the model flexibility to balance supply and demand to obtain a high level of valorisation of the raw

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material. The hubs provide the demand-driven quantity to Department X. This is the quantity demanded by the customers of CX, which is equal to the fixed and reducible quantity. Ideally, this is the quantity which CX will produce. However, CX has the obligation to process all supplied raw material. Unfortunately, the supply of raw material usually does not match the raw material needed to fulfil the demand. With a raw material shortage, Department X should cut into the production quantities. The amount which can be cut is the reducible demand. With a raw material surplus, Department X should plan extra production to process all raw materials, which are called supply- driven quantities. The amount which is produced extra is the additional segment. The system with the three segments is visualised in Figure 2.2.

Figure 2.2 - The demand system with three segments

We must note that not all products have three segments. Profitable products only have a fixed demand which is usually equal to the production capacity. These products should not be reduced, because they add a lot of value. An additional demand is not possible, because the production is already limited by its production capacity.

2.5. Supply chain in the S&OP tool

The S&OP model is an aggregated model and therefore a simplified version of the actual supply chain of CX. All main characteristics are present in the model, among others the raw material supply, factories, products, machines, transport costs, inventory costs, operational costs, capacity constraints and customers. Considering interdependence of the factories and the various products, the S&OP model can be characterized as a multi-echelon, multi-product supply chain model.

In the model, the supply chains of all ‘hubs’ are modelled. Hubs are the S&OP divisions of CX, which manage their own product category (e.g. product 1 or product 2) and corresponding supply chain.

The supply chains show some overlap, because factories often produce multiple products of different categories. For example, a factory produces product 1 and product 2. Therefore, hubs are not location specific and multiple hubs can manage one factory. The supply chain of each hub is modelled in the S&OP model.

Figure 2.3 is a visualisation of the modelled supply chain of a hub. Each hub is modelled similarly with its own products. The beginning of the supply chain is the supply of raw material. The raw material is allocated to different machines at different factories. Each machine can have one or more operations which process raw material into main products and by-products. There is an operation for each machine-main product combination. The product lines from each machine to the main products illustrate which products a machine can make. Most of the machines have one operation, but the machines in factory 1 have two operations; they can make both product 1 and product 6. The product lines of each machine to the by-products are not visualised in Figure 2.3 to maintain overview. All operations in the supply chain produce the by-products product 3 and product 4. The operations are modelled as one aggregated version of the actual processes, which actually consists of multiple successive operations. By-products of each hub are exchanged with other hubs. Other hubs use these by-products as input in their production processes. For example, product 4 is further processed into product 7 and product 9. The main products go through a fictional distribution centre

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to distribute the products from different factories to the customers. The model is not allowed to hold any stock throughout the months.

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Figure 2.3 - Structure of the modelled supply chain

The actual customers of CX are not modelled in the S&OP model. What is modelled, are hub specific customers. In the model, the hub has a ‘customer’ for each segment, i.e. a fixed, a reducible and an additional customer. This is necessary in order to assign different sales prices at different production levels to a product. The sales prices and quantities of products are linked to a specific customer with a forecast item. Each customer has a different priority regarding the fulfilment of the demand of its products. Fixed demand has an extremely high penalty when their demand is not fulfilled. The reducible demand has a low penalty when their demand is not fulfilled and the additional demand does not involve a penalty. This is consistent with the situation of the three segments. Because of the extremely high penalty, the fixed demand should always be fulfilled. The reducible demand can be reduced and due to the low penalty, it is prevented that when de reducible and additional sales prices are equal, the additional demand is fulfilled instead of the reducible.

2.6. Valorisation and equivalence tables

When including price elasticity in the model, it affects the valorisation, or added value, of product 1.

Increasing the production quantity decreases the valorisation per ton product 1 due to the decrease in sales price. Because the S&OP model aims for the best financial performance and thus for the highest valorisation, it is important to have insight into the valorisation of products to understand the decision-making of the model.

To measure the valorisation of a product, not only the main product should be considered, but also by-products like product 3 and product 4. Therefore, Department X has divided its products into so- called ‘baskets’, such as a product 1 basket with product 3 and product 4 and a product 2 basket with product 4 as by-product. With these baskets, Department X can compare the valorisation of its products.

For the calculation of the valorisation, Department X considers the revenue, recipe costs and production costs for the main and the by-products. Recipe costs are the costs of added components to produce the end products. The cost of supplied raw material is the only important component which is left out of the calculation of the valorisation. These costs are not considered, because CX determines the raw material price and therefore, the cost of supplied raw material. CX uses the valorisation of its products is input for determining the raw material price. Figure 2.4 represents the basic calculation of the valorisation of a basket.

Figure 2.4 - Basic calculation for the valorisation

To determine the output quantity and recipe costs, CX uses a dynamic bill of materials (BOM). This BOM is dynamic, because the composition of raw material has a seasonal pattern. The composition of raw material influences the output quantity. To compare the valorisation of products, Department X uses an equal unit of measure. They calculate the valorisation of a basket based on 1 ton of raw material intake. The forecast of the valorisation of the baskets for the coming months are reported in equivalence tables (ETs). Figure 2.5 shows an example of an ET with the five baskets. We see that the valorisation of each basket changes throughout the months. There are two main causes for these

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changes: market developments and the composition of raw material. Changing market conditions influence the sales price of the main and by-products.

Figure 2.5 - Example of an equivalence table

The valorisation of the baskets is important for balancing supply and demand. With a shortage in the raw material supply, the production of the basket with the lowest valorisation should be reduced.

With a raw material surplus, the production of the best valorising basket should be increased. In the ET we see that product 11 is the best valorising basket, while product 2 is the worst valorising basket.

2.7. Conclusion

In this chapter, we investigated the current situation at CX. With this chapter, we answer our first research question:

How does Company X currently manage demand in the S&OP process?

Our investigation concludes that:

• The currently used revenue curve is linear, while the actual revenue curve is concave. This can lead to sub optimal decisions in the S&OP plan.

• The concave revenue curve results from the characteristics of the oligopolistic market of product 1 and the market share of CX. This effect is not observed in the product 2 market.

• The S&OP tool of CX consists of multiple coherent tables and a linear solver. Therefore, piecewise linear approximations are necessary to implement price elasticity.

• The demand in the S&OP model is divided into three segments, i.e. the fixed, reducible and additional segment.

• The supply chain in the S&OP model is modelled according to the aggregated supply chain of each hub and with a ‘customer’ for each demand segment.

• The forecast of the added value of the products of CX are reported in equivalence tables, which show the valorisation of 1 ton raw material into a ‘basket’, consisting of one main product and corresponding by-products.

In the following chapters, we further investigate the impact of using the actual concave revenue curve. We adjust the current demand and supply chain model and apply piecewise linear approximations. We use the calculations of the valorisation in the equivalence tables in this research to financially analyse the effects of price elasticity.

Before we investigate the influence of price elasticity within CX, we review scientific literature about the effects of price elasticity in sales and operations planning. We also describe the literature about piecewise linear approximations, because this is necessary to implement price elasticity in the S&OP model.

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3. Literature research

In this chapter, we study scientific literature relevant to the research project. The literature study is twofold. First, we perform a literature review to investigate the status of research about the use of price elasticity within sales and operations planning. Second, we perform an explorative study about piecewise linear approximations. Ultimately, we provide an answer to the second research question:

What literature is available related to the use and implementation of price elasticity in sales and operations planning of Company X?

3.1. Price elasticity in sales and operations planning

To provide a comprehensive answer to the question, we use a systematic literature review protocol to select relevant literature. Appendix A shows the review protocol. The concept matrix with the key findings is reported in Appendix B. We combine sales and operations planning with price elasticity and oligopolistic markets. We focus on the oligopolistic markets, because the product 1 market is considered as an oligopolistic market. Figure 3.1 visualises the

overlap between the topics. Not a lot of literature all three exists that combines concepts together. To overcome this issue, we look for literature that combines sales and operations planning with the other topics (combination A and B). Because we are only interested in the impact on the sales and operations planning, we exclude the combination of oligopolistic markets and price elasticity (combination C) from our review. We first give a description of the concepts of the literature review. Then we discuss the impact of price elasticity on the sales and operations planning.

Sales and operations planning

Sales and operations planning (S&OP) is a planning process that combines different business plans into one integrated set of plans (Thomé, Scavarda, Fernandez, & Scavarda, 2012). The purpose of S&OP is to balance or integrate demand and supply plans at an aggregate level, usually on a monthly basis (Feng, D’Amours, & Beauregard, 2008; Wallace & Stahl, 2008; Thomé et al., 2012). S&OP uses aggregate data, such as clusters of resources and product families, rather than individual stock keeping units (Grimson & Pike, 2007; Noroozi & Wikner, 2016). S&OP should be a cross-functional process in which different functions, such as sales and marketing, production, purchasing, finance, human resources and product development should cooperate and agree on the final plan (Wallace &

Stahl, 2008). Due to the alignment of plans and performances of different functions, S&OP supports the business strategic plan and can lead to improvements in profit customer satisfaction and organizational atmosphere (Chen & Chen, 2008; Feng et al., 2008). The participation of people is very important for a successful execution of the S&OP process (Grimson & Pike, 2007). The suggested planning horizon of an S&OP process is between three months and three years (Grimson & Pyke, 2007). Nevertheless, most researchers emphasize on the horizon of between 12 and 18 months (Wallace & Stahl, 2008), especially for companies with a seasonal profile (Grimson & Pike, 2007).

S&OP can increase the profitability of the supply chain, because supply and demand are matched in a coordinated process. Supply is managed by using capacity, inventory, subcontracting and backlogs.

Demand is managed by using short-term price discounts and promotions (Chopra & Meindl, 2013).

To summarizS&OP, Thomé et al. (2012, p. 2) described the main features of S&OP as follows:

• It is a cross-functional and integrated tactical planning process within the firm

• It integrates all the plans of the business in a unified plan

• It has a planning horizon from less than three months to over 18 months

• It bridges strategy and operations

• It creates value and is linked with the performance of the firm

Figure 3.1 - Overlap between the topics

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Page 11 Oligopoly

An oligopoly is an industry characterized by a few dominant firms, each large enough to influence the market price. Products in an oligopolistic market may be homogenous or differentiated. Companies in an oligopolistic market do not only compete in price, but also in marketing and new products (Case et al., 2011).

A lot of different models from the fields of game theory and competitive strategy are developed to increase profitability in an oligopoly. A simple and common model is the Cournot model, introduced by the mathematician Antoine Augustin Cournot in the 19^th century (Case et al., 2011). In the Cournot model, all firms produce a homogeneous product and compete in production quantities.

Product prices are variable functions of the collective market supply. Therefore, companies do not control prices, but they influence them with their production decisions (Tominac & Mahalec, 2017).

Companies set optimal production quantities to maximize their profit, given their competitors production quantities (Ma, Zhu, & Wang, 2013).

Price elasticity

The law of demand states that a decrease in product price leads to increase in product demand and vice versa. Price elasticity is the concept which expresses the degree of responsiveness between the sales price and the demand of a product (Lui, Shah, & Papageorgiou, 2012). Price elasticity is defined as the ratio of the percentage change in quantity to the percentage change in price (Case et al., 2011).

Impact of price elasticity in S&OP

Now we have identified the concepts within the research topic, we try to investigate the impact when these concepts come together. Table 3.1 presents the effects of including price elasticity on the profit, revenue, production quantity and sales price according to the articles which are reviewed in the systematic literature review.

Aspect of the operations

Increased Decreased Stable Not considered

Profit Algarni et al. (2007), Calfa &

Grossmann (2015), Chen &

Chen (2008), Hjaila et al.

(2014), Kaplan et al. (2011), Lui et al. (2012), Ma et al.

(2013), Tang et al. (2015), Tominac & Mahalec (2017)

Karmarkar & Rajaram (2012)

Farris & Darley (1964)

Revenue Calfa & Grossmann (2015), Kaplan et al. (2011), Tang et al. (2015), Tominac &

Mahalec (2017)

Karmarkar & Rajaram (2012), Lui et al. (2012)

Hjaila et al.

(2014)

Algarni et al.

(2007), Chen &

Chen (2008), Farris

& Darley (1964), Ma et al. (2013) Quantity Calfa & Grossmann (2015),

Kaplan et al. (2011), Tang et al. (2015), Tominac &

Mahalec (2017)

Karmarkar & Rajaram (2012), Lui et al. (2012)

Algarni et al. (2007), Hjaila et al.

(2014)

Chen & Chen (2008), Farris &

Darley (1964), Ma et al. (2013) Sales price Lui et al. (2012), Ma et al.

(2013)

Calfa & Grossmann (2015), Kaplan et al.

(2011), Karmarkar &

Rajaram (2012), Tominac

& Mahalec (2017)

Farris &

Darley (1964), Hjaila et al.

(2014)

Algarni et al.

(2007), Chen &

Chen (2008), Tang et al. (2015)

Table 3.1 - Classification of the effects of price elasticity

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Page 12

In Table 3.1, we see that in most cases the profitability of a supply chain increased when price elasticity is included in the operations planning, especially with a very elastic market (Chen & Chen, 2008; Kaplan, Türkay, Karasözen, Biegler, 2011; Lui et al., 2012). Besides that, in most articles the revenue increased because of higher production quantities and lower prices. In the case of Lui et al.

(2012), the revenue and quantity decreased, but due to higher prices, the profit increased.

Production planning in an oligopolistic market can benefit from the analysis of the behaviour of competitors (Tominac and Mahalec, 2017).

Nevertheless, we cannot translate the results towards our research, because a complex supply chain network makes it difficult to understand the system response to price elasticity (Kaplan et al., 2011).

Besides that, the approach used to approximate the revenue curve can significantly affect the decision-making and the economic behaviour of the supply chain (Hjaila, Zamarripa, Shokry, &

Espuña, 2014). The research of Hjaila et al (2014) and Calfa and Grossmann (2015) both observed that more complex models which are closer to the real price behaviour provide better solutions and economic advantages relative to simpler and less accurate models, especially when the demand is price sensitive. Therefore, an accurate model is important to make financially optimal decisions.

However, more complex models required larger computational effort and resources information flows should be integrated in the process (Hjaila et al., 2014).

Besides the effects in Table 3.1, authors also considered costs (Algarni et al., 2007; Hjaila et al., 2014) which decreased in those cases. Inventory was also considered, which decreased in the study of Calfa and Grossmann (2015) and with the study of Lui et al. (2012), the inventory deviation decreased.

3.2. Piecewise linear approximations

The S&OP tool of Company X can only process linear data. Unfortunately, the revenue function determined by Van Haperen (2016) is a quadratic function (Section 1.1). To implement price elasticity in the S&OP model, Van Haperen suggested to linearize the function by using piecewise linear approximations. In this section, we investigate available literature about computational methods for piecewise linear approximation to support our research.

Piecewise linear approximations are widely used to approximate non-linear functions, also in the field of planning and scheduling, supply and demand curves, and in the allocation of resources in general (Keha, de Farias Jr., & Nemhauser, 2004; Kontogiorgis, 2000). In general, a piecewise linear function consists of multiple linear line segments K over the interval [l, u] (Yamamura & Tamura, 2012). The two end-points of each segment are called breakpoints. The slope of the function changes at each breakpoint (Winston, 2004). The most common approach to compute a piecewise linear function is through linear interpolation between sample coordinates, because it preserves the concavity and continuity of the nonlinear function (Kontogiorgis, 2000; D’Ambrosio, Lodi, & Martello, 2010). Figure 4.2 illustrates an example of a nonlinear function and its piecewise linear approximation with three segments.

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Page 13

Figure 3.2 - Example of a piecewise linear approximation

The accuracy of an approximation is mainly based on the number of linear segments. The accuracy increases when increasing the number of segments in an interval. However, more segments also require more computational effort (Keha et al., 2004). Barros and Weintraub (1986) report 14 uniform segments provide the adequate accuracy for the approximation of supply and demand functions of sugar and wheat. Experimentation shows that 5 to 10 segments is a proper approximation for airline revenue curves (Curry, 1990).

Besides the number of segments, also the placement of the breakpoints has influence on the accuracy of the approximation. The placement of the breakpoints is usually left to the domain expertise and skill of the modeller (Kontogiorgis, 2000). However, the optimal placement can be calculated objectively. Where the magnitude of the curvature is greater, an approximation needs more breakpoints for the same accuracy (Kontogiorgis, 2000). The curvature can be expressed with the second derivative. In the case of a quadratic function is the second derivative constant.

Therefore, an equal distribution of the breakpoints is optimal (Kontogiorgis, 2000).

Now, we elaborate about the general appraoch of linear interpolation to compute the piecewise linear function of the quadratic function over the interval [l, u]. The approach is based on to the method used by Yamamura and Tamura (2012) and similar to the methods of Kontogiorgis (2000), Keha, de Farias Jr. and Nemhauser (2004) and D’Ambrosio, Lodi and Martello (2010).

For the number of breakpoints we take = ⋯ = . The piecewise linear function is linear for the segments [aj-1, aj] for = 1, 2, … , . When we determined the segments, we take samples of at the breakpoints :

= ! " #$ 0,1, … , (3) Now, we introduce the auxiliary variables δ to formulate and .

The value of δ satisfies:

• 0 ' δ ' (

• If δ 0 1 ' ) ' 1 , then δ * 0

• If 0 δ₊ ₊ ₊₍ 1 ' ) ' 1 , then δ ₍ for 1 ' ' ) 1 and δ 0 for ) 1 ' '

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Page 14 Then, every value of in [l, u] can be written as:

+ δ + δ +⋯ δ (4)

With the linear interpolation between the samples we can finish the general computational approach for the piecewise linear functions. can be written as:

δ + −

− δ +⋯ ⁽

( δ (5)

3.3. Conclusion on the literature study

In this literature study, we reviewed literature about the impact of using price elasticity in sales and operations planning and studied literature about piecewise linear approximations. Therefore, this chapter provides the answer to our second question:

What literature is available related to the use and implementation of price elasticity in sales and operations planning of Company X?

According to literature, we found the following about price elasticity in sales and operations planning:

• The profitability of a supply chain improves in most cases by using the concept of price elasticity, especially in markets with a high price elasticity.

• Production planning in an oligopolistic market benefits from the analysis of the behaviour of competitors.

• A complex supply chain makes it difficult to understand the response to price elasticity.

• Models which are closer to the real price behaviour provide better solutions and economic advantages relative to less accurate models.

We also studied literature about piecewise linear approximations. We conclude that:

• We have a general approach for piecewise linear approximations, which we adopt for the implementation of price elasticity in the S&OP model.

• An accurate approach to approximate the revenue curve is important to make financially optimal decisions for the production quantity.

• The main factor for the accuracy of the approximation is the number of segments; more segments provide a higher accuracy.

• Approximations with 5 to 14 segments provide adequate accuracy for the approximation of supply, demand and revenue functions.

Literature is promising about the implementation of price elasticity. However, it does not offer a direct solution to our research. Therefore, we further investigate the implementation of price elasticity in the S&OP process of CX. Several articles confirm that the approach to model price elasticity is an important factor. In the next chapter, we further analyse how we approach price elasticity and construct our model with piecewise linear approximations. Furthermore, we perform experiments in Chapter 5 with the number of segments, because this is an important factor for the accuracy of the approximation.

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4. Model adjustment

In this chapter, we investigate how we can approach price elasticity and construct the S&OP model in a way it considers the price elasticity of product 1. We also define key performance indicators to analyse the results. We answer our third research question:

How should we adjust the S&OP model to implement the price elasticity of product 1?

4.1. Influences in the market

At first, we elaborate about the influences in the product 1 market which we consider in this research. The main influence is the production quantity of product 1 of CX. We also consider two other factors, the sales of raw material to competitors and the production of product 5.

As mentioned in Section 1.2, CX observes that the production quantity of CX has influence on the price in the product 1 market. The quantity and price form together the revenue of CX. The production of product 1 increases the quantity. The increase in quantity increases the revenue of product 1. An increase in quantity also leads to a decrease in price, which decrease the revenue.

We also find another effect on the revenue, the additional sales of raw material. Not all raw material supplied is processed by CX; some raw material is sold to competitors. CX sells a fixed quantity of raw material to competitors, because they have a contractual agreement. On top of that, CX sells additional quantities when the factories do not have the capacity to process the raw material supply in its own factories. These additional quantities are mainly processed into product 1 and increase the total volume in the market. According to the market analyst of FC, 60 to 100 percent of the additional raw material sales end up in product 1. Therefore, the additional sales of raw material affect the market price of product 1.

Before selling raw material, CX first tries to allocate the raw material to its own factories. One of these products is product 5. The product 5 market has a fixed demand, but CX can produce additional volumes. In that case, CX drives other competitors of the market. Instead of product 5, competitors process 60 to 100 percent of the raw material into product 1. Therefore, each unit of raw material used to produce additional volumes of product 5, leads to the same amount of raw material available at competitors. This behaviour affects the product 1 market in the same way as additional raw material sales. Because the effect of product 5 is equal to the raw material sales, we include the effect of product 5 within the sales of raw material. The effects on the product 1 market are visualised in Figure 4.1.

CONFIDENTIAL

Figure 4.1 - Influence on revenue of product 1

4.2. Including raw material sales

In this section, we elaborate further about the effect of raw material sales and product 5. As mentioned in Section 4.1, 60 to 100 percent of the additional raw material sale is processed into product 1 by competitors. We define this ratio as the ‘raw material-product 1 ratio’. The exact ratio is unknown and varies per month. The additional production of product 5 has a similar effect as raw material sales and is included in the additional raw material sales.

The quantity of product 1 which is produced by competitors depends on a few variables. Because we deal with additional raw material sales, the initial volume 0. The change in raw material sales (∆ is equal to the total quantity of additional raw material sales . Then, we can express the relation between additional raw material sales and the change in quantity of the product 1 market (∆ , through the following equation:

∆ , , ∗ BOM ∗ QR (6)

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Page 16 In which:

∆ , = Change in quantity of the product 1 market by competitors , = Raw material-product 1 ratio

BOM = Amount of product 1 which can be produced from one unit of raw material QR Quantity of the raw material which is sold additionally to competitors

Because the change in the price of product 1, ∆ −∆ , ∗ , the change in price of product 1 due to the raw material sales is:

∆ −, ∗ BOM ∗ QR ∗ (7)

Because a change in revenue by a change in price can be expressed with ∆ ∗ ∆ , the effect of raw material sales on the revenue of product 1 of CX is:

∆R Q ∗ , ∗ BOM ∗ QR ∗ (8)

From (8), we see that both the quantity of additional raw material sales and the quantity of product 1 are factors which determine the influence of raw material sales on product 1. Because of this interdependence is the relationship between raw material sales and product 1 complex.

To calculate the influence, both the quantity of raw material sales and product 1 should be known.

Unfortunately, both are decision variables determined by the S&OP model. It is impossible to implement this complexity into the S&OP tool, because we cannot model a price dependent on a variable quantity of another product. To implement the influence in the S&OP tool, we need to make the revenue dependent on one of the quantities and assume the other.

When we assume the quantity of product 1, we can include the effect in the price of raw material sales. When we assume the quantity of raw material sales, we can include the effect in the price of product 1. From the experience of the S&OP planners, the production of product 1 is rather stable, while the quantity of additional raw material sales is far more volatile. This is the case because the sale of raw material is used as the final option when the raw material supply exceeds the capacity of the factories of CX. Due to the volatility, it is better to assume the quantity of product 1 than the quantity of raw material sales.

For the assumption of the product 1 quantity, we can take . From (8) we can derive the effect on the product 1 revenue when is increased with one unit, which should be the offset in the price of raw material sales ∆ :

∆ ∆

∆ Q ∗ , ∗ BOM ∗ (9)

Because ∆ , we can write the price of raw material sales :

PR − , ∗ BOM ∗ Q ∗ (10)

Now we have included the influence of raw material sales and product 5 on the revenue of product 1 in the sales price of the raw material. With (10), we can determine the adjusted price of raw material sales. The raw material price is not dependent on the quantity of the raw material sales, so the price remains constant for all quantities. Because this effect is included in the price of raw material, the revenue function of Section 1.1 stays unchanged.

The exact value of the raw material-product 1 ratio is unknown, but it is somewhere between the 60% and 100% according to the market analyst of CX. Therefore, we propose to experiment with multiple ratios to provide insight into the influence of raw material sales.

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Page 17

4.3. Computation of the approximation

In this section, we investigate the characteristics of the piecewise linear approximation. First, we determine the placement of the breakpoints. Then, we adjust the approximation and establish bounds of the approximation. At last, we describe the tool which automates the calculations.

Placement of breakpoints

The placement of the breakpoints has influence on the accuracy of the approximation. The placement of the breakpoints is usually left to the domain expertise and skill of the modeller (Kontogiorgis, 2000). However, we want to determine the placement objectively. Where the magnitude of the curvature is greater, an approximation needs more breakpoints for the same accuracy (Kontogiorgis, 2000). We can express the curvature of a function with the second derivative.

The second derivative of the revenue function (Section 1.1: ∗ ∗ ∗ ) is:

′′ 2 (11)

This means that the curvature is only dependent on the elasticity value, which is constant. Because the curvature is constant, the optimum placement of the breakpoints is uniform. Therefore, we get an equal deviation and accuracy at all segments of a piecewise linear approximation.

Underestimation and overestimation

Since the revenue curve is concave, the piecewise linear approximation always underestimates the revenue, except from the breakpoints. Ideally, piecewise linear approximation should underestimate as much as it overestimates the revenue. In other words, the piecewise linear approximation should estimate the revenue with an average deviation of zero.

Because all segments have the same absolute deviation, we can obtain an average deviation of zero by increasing the initial value of the piecewise linear function (i.e. ). When the surface of deviation above the linear approximation is equal to the surface below the linear approximation, the average deviation is zero (see Figure 4.2a).

Figure 4.2 - The underestimation equal to the overestimation (a) and the maximum deviation in the middle of a segment (b)

To adjust all piecewise linear curves without loss of generality, we want to use a ratio relative to the maximum deviation. The maximum deviation of an unadjusted piecewise linear approximation of quadratic function is exactly in the middle of each segment, which is illustrated in Figure 4.2b. The ratio to adjust to obtain an average deviation of zero is 2 35 . The proof of this ratio is given in Appendix C. The value of b0 is as follows:

2

3 ∗ 6 786 6 9:;8 <8#= (12)

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Page 18 Bounds of the approximation

In this section, we establish a lower and an upper bound. We determine these limits because it is not necessary to compute the piecewise linear approximation over an extremely large range. We only approximate the relevant area, because this provides the information we need and prevents unnecessary computational or human effort. Figure 4.3 shows two approximations of the revenue curve with three segments. We see that the approximation with bounds provides a higher accuracy in the relevant area than the approximation without bounds.

Figure 4.3 - Approximations in the relevant area

We choose a lower bound, because CX will certainly produce a minimum amount of product 1.

According to historic data, CX not produced less than 3,000 tons a month in the past years. A lower production is not desirable, because it can possibly disappoint customers and CX can lose market share. Therefore, we take 3,000 tons per month the lower bound.

For the upper bound we consider the production capacity. CX has a certain production capacity for product 1 which cannot be easily increased in the tactic horizon of the S&OP process. The production capacity of product 1 varies per month due to a varying amount of available production hours in the factories. Another factor is that the production lines of factory 1 produce both product 1 and product 6. The production of the more valorising product 6 limits the production capacity of product 1.

Therefore, the maximum capacity for a month cannot exceed 4,800 tons and we take that as upper bound.

Now we have the bounds, we model a large segment for the quantity of 0 to 3,000 tons and multiple segments in the range from 3,000 tons to 4,800 tons. In this case, the quantity and revenue can be implemented correctly in the S&OP model.

Computation of piecewise linear approximations

For this research, we need to compute piecewise linear approximations of product 1 for all 18 months of the planning horizon of the S&OP tool. When experimenting with the number of segments, we need to compute 18 piecewise linear approximations for each experiment. To prevent lots of human effort for the calculation, we automated the process into a tool. The tool is coded as a macro written in Visual Basic for Applications, for use within Microsoft® Excel (Office 2010). The outputs of the tool are the sizes of the segments and corresponding sales prices for each month. The inputs for the calculations are:

• Number of segments

• Lower bound

The impact of price elasticity in the sales and operations planning

Bachelor Thesis